For Magnetic Softness in Nanostructures

The most prominent contribution to the magnetic anisotropy energy is determined by the symmetry axis of the local atomic structure (Ch. 3). The free energy density eK of this magnetocrystalline anisotropy can be expressed, for example, by 

The anisotropy fluctuations (AK) discussed above typically result from fluctuating orientations of the magnetic easy axis which varies from one grain to another in conventional polycrystalline microstructures, though Eq. (1) is not limited to this mechanism of anisotropy fluctuations. Hence, for conventional polycrystalline materials where 4 Lcx, the parameter AK introduced into Eq. (1) can be well approximated by the magnetocrystalline anisotropy constant Kh However, as we discuss in the subsequent section, the approximation of AK by K is no longer applicable for small structural correlation lengths. 

The angle W in Eq. (5b) represents the resulting easiest axis of the N exchange coupled grains. It is still a random variable which fluctuates on the scale of Lex from one set of N coupled grains to the other. Accordingly, the conditions AK K and /K Lex are relevant to the relationship in Eq. (1) for D L0 and hence, the coercivity Hc is expected to be proportional to K . 

This renormalization means that the exchange correlation length expands at the same time as the anisotropy is averaged out. By combining Eqs. (6) to (8) we finally get [2, 11] 

The prefactor introduced in Eqs. (3) and (8) remains the open parameter within the above scaling analysis. A theoretical determination of Po would ultimately require a by far more complex micromagnetic analysis of the problem. It is therefore best to estimate pa from experiment from the upper critical grain size where coercivity no longer follows a D6 law and tends to reach its maximum (cf. Fig. 4). This yields po 1.5 for Fe-Si-B-Nb-Cu type alloys and is consistent with rough theoretical estimates [28]. 

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Abstract The focus of this chapter is primarily directed towards nanocrystalline soft magnetic materials prepared by crystallization of amorphous precursors. The key elements involved in the development of this class of materials are three-fold (i) theoretical models for magnetic softness in nanostructures (ii) nanostructure-property relationships and (iii) nanostructural formation mechanisms. This chapter surveys recent research on these three areas with emphasis placed on the principles underlying alloy design in soft magnetic nanostructures. 

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